Very old university — get irritated about ending of generous grant (9)
I believe the answer is:
vouchsafe
'grant' is the definition.
(I know that vouchsafe is a more specific form of the action grant)
'very old university get irritated about ending of generous' is the wordplay.
'very old university' becomes 'vou' (this might be a standard abbreviation I've not previously seen).
'get irritated' becomes 'chafe' (to chafe is to become sore or irritated).
'about' is an insertion indicator.
'ending of' says to take the final letters.
The last letter of 'generous' is 's'.
'chafe' placed around 's' is 'chsafe'.
'vou'+'chsafe'='VOUCHSAFE'
(Other definitions for vouchsafe that I've seen before include "Give in gracious manner - have focus on" , "Condescend to grant" , "Give or grant, perhaps in condescending manner" , "Grant graciously" , "Deign to give" .)